In this paper, the problem of resource allocation optimization is studied for a single-cell multiuser cognitive radio network in the presence of primary user networks. The spectral access of the cognitive radio network is based on Orthogonal Frequency Division Multiple Access (OFDMA). A joint bandwidth and power allocation is performed so that users' rate requirements are satisfied, and the integrity of primary user communication is preserved. In this work, two unique challenges are addressed. The first is the incorporation of primary user activity in the design of resource allocation technique, and the second is the limited hardware capabilities of cognitive terminals compared to those available at the cognitive base station. To address these problems, a novel resource allocation framework is proposed based on the bandwidth-power product minimization, which is an effective metric in evaluating the spectral resource consumption in a cognitive radio environment. The framework takes into consideration the challenges aforementioned. The results show significant enhancement in spectral efficiency by using our framework compared to classical power adaptive optimization using iterative waterfilling scheme.